QuestionDecember 25, 2025

24. What is the factored form of 27p^3-8q^3 (3p-2q)(9p^2+6pq+4q^2) (3p-2q)(3p-2q)(3p-2q) (3p+2q)(9p^2-6pq+4q^2) (3p+2q)(9p^2-12pq+4q^2)

24. What is the factored form of 27p^3-8q^3 (3p-2q)(9p^2+6pq+4q^2) (3p-2q)(3p-2q)(3p-2q) (3p+2q)(9p^2-6pq+4q^2) (3p+2q)(9p^2-12pq+4q^2)
24. What is the factored form of 27p^3-8q^3
(3p-2q)(9p^2+6pq+4q^2)
(3p-2q)(3p-2q)(3p-2q)
(3p+2q)(9p^2-6pq+4q^2)
(3p+2q)(9p^2-12pq+4q^2)

Solution
3.8(256 votes)

Answer

(3p-2q)(9p^{2}+6pq+4q^{2}) Explanation 1. Identify the formula for factoring a difference of cubes Use **a^3 - b^3 = (a-b)(a^2 + ab + b^2)**. 2. Express 27p^3 - 8q^3 as a difference of cubes 27p^3 = (3p)^3, 8q^3 = (2q)^3. So, a = 3p, b = 2q. 3. Apply the formula Substitute into the formula: (3p-2q)((3p)^2 + (3p)(2q) + (2q)^2). 4. Simplify the second factor (3p)^2 = 9p^2, (3p)(2q) = 6pq, (2q)^2 = 4q^2. So, 9p^2 + 6pq + 4q^2.

Explanation

1. Identify the formula for factoring a difference of cubes<br /> Use **$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$**.<br />2. Express $27p^3 - 8q^3$ as a difference of cubes<br /> $27p^3 = (3p)^3$, $8q^3 = (2q)^3$. So, $a = 3p$, $b = 2q$.<br />3. Apply the formula<br /> Substitute into the formula: $(3p-2q)((3p)^2 + (3p)(2q) + (2q)^2)$.<br />4. Simplify the second factor<br /> $(3p)^2 = 9p^2$, $(3p)(2q) = 6pq$, $(2q)^2 = 4q^2$. So, $9p^2 + 6pq + 4q^2$.
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